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2024 International Russian Automation Conference, RusAutoCon 2024

作者： Solodusha, Svetlana Markova, Evgeniia Kokonova, Yuliya Melentiev Energy Systems Institute Sb Ras Irkutsk Russia Matrosov Institute for System Dynamics and Control Theory Sb Ras Irkutsk Russia Irkutsk National Research Technical University Irkutsk Russia

The paper presents algorithms for constructing nonlinear integral models based on the Volterra series tool. Modeling of dynamic processes means assessing the response to possible external changes in real time. The vector of input signals may include measured influences and control actions to be identified based on an analysis of the current state. We use identification algorithms based on the theory of Volterra polynomial equations of the first kind. An approach to the approximate solution to selected types of nonlinear systems of Volterra integral equations using the Newton-Kantorovich method is presented. We use the numerical solution to the corresponding linear system of equations as a trial solution. Calculation schemes obtained with help the standard quadrature methods are given. © 2024 IEEE.

关键词： Integral equations

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Monowave Boundary Construction Method for the Non-convex Reachable Set of the controlled Dynamical system 1

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7th International Conference on Optimization, Simulation and control, COSC 2022

作者： Zarodnyuk, Tatiana Gornov, Alexander Matrosov Institute for System Dynamics and Control Theory of SB RAS Irkutsk Russia Moscow Institute of Physics and Technology Dolgoprudny Russia

ISBN: (数字)9783031412295

ISBN: (纸本)9783031412288

The paper proposes a computational technology for constructing the boundary of the reachable set of the controlled dynamical systems. The monowave method underlying it relies on the use of a given sequence of controls with a moving switching point. To construct the controls of a given structure, the time interval is divided into equal parts. Then controls are built in the form of relay functions with switching points in the nodes of the generated grid. A series of computational experiments was carried out to construct the boundaries of non-convex reachable sets. The obtained results made it possible to demonstrate the effectiveness of the proposed monowave method. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023.

关键词： Dynamical systems

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Semi-supervised K-Means Clustering via DC Programming Approach 22nd

Semi-supervised K-Means Clustering via DC Programming Appro...

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22nd International Conference on Mathematical Optimization theory and Operations Research, MOTOR 2023

作者： Gruzdeva, Tatiana V. Ushakov, Anton V. Matrosov Institute for System Dynamics and Control Theory of SB RAS 134 Lermontov str. Irkutsk664033 Russia

ISBN: (纸本)9783031353048

Though clustering is related to unsupervised machine learning and does not require any prior information on data items, in many real-life settings, there may be some expert knowledge on data labels or the properties of clusters known in advance. Obviously, such knowledge may be used to guide clustering process and improve the quality of found partitions. The clustering problems that involve some additional information on tags are called semi-supervised or constrained clustering problems. One distinguishes instance-level and cluster-level constraints usually formalized as the so-called must-link and cannot-link constraints or minimum/maximum cluster size. In this paper, we consider the constrained minimum sum-of-squares (k-means) clustering (MSSC) problem that incorporates both instance- and cluster-level constraints. As far as we know, such a semi-supervised MSSC problem has not been considered in the literature yet. We formulate this clustering problem and some of its particular cases as DC (difference of convex) optimization problems. Then, we develop a solution approach based on a special local search method. We carry out computational experiments on test problem instances demonstrating the efficiency of the proposed solution approach. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： K-means clustering

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Implicit Boolean Network for Planning Actions 45

Implicit Boolean Network for Planning Actions

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45th Jubilee International Convention on Information, Communication and Electronic Technology, MIPRO 2022

作者： Oparin, G.A. Bogdanova, V.G. Pashinin, A.A. Matrosov Institute for System Dynamics and Control Theory of Sb Ras Irkutsk Russia

ISBN: (纸本)9789532331035

It is usual to classify the automated searching of a plan as an artificial intelligence problem. In planning, the environment is defined as a set of both states and transitions between them. Planning consists in searching for a finite transitions sequence (actions) that transfers the initial state to one of the states, satisfying the objective. As a model of the planning environment, we propose to use implicit Boolean networks - binary dynamic systems, the transition function of which is defined by the implicit Boolean equation relative to the current state variables vector and some subsequent variables vectors. For this model, the forming of a plan is reduced to qualitative analysis of dynamic properties of the implicit binary dynamic system. In particular, these are reachability or cyclicity properties over a given discrete time interval. At the final stage of this method, the verification of the Boolean formula satisfiability is performed. This formula includes the equation of the dynamics of the implicit Boolean network and the specification of the dynamical property being verified. The considered approach is demonstrated on the problem of planning a river crossing and constructing a Hamiltonian cycle in a graph. A specialized parallel algorithm for solving deeply structured Boolean satisfiability problems is proposed, which provides scalability with an increase in their dimension. © 2022 Croatian Society MIPRO.

关键词： Hamiltonians

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Speeding up the Solving of Logical Equivalence Checking Problems with Disjunctive Diagrams 46

Speeding up the Solving of Logical Equivalence Checking Prob...

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46th ICT and Electronics Convention, MIPRO 2023

作者： Kondratiev, Victor Otpuschennikov, Ilya Semenov, Alexander ITMO University St. Petersburg Russia Matrosov Institute for System Dynamics and Control Theory SB RAS Irkutsk Russia

ISBN: (纸本)9789532331042

In the context of the problem of checking the equivalence of Boolean circuits (LEC), we propose an approach that increases the efficiency of modern SAT solvers on this problem by generating additional constraints of a special kind. To generate such constraints, we use a variant of decision diagrams called disjunctive diagrams. In contrast to well-known Binary Decision Diagrams these diagrams can be constructed effectively for an original formula and can also be used to extend the original CNF formula with new clauses which are its logical consequences. In computational experiments, we show that the resulting formulas, encoding difficult LEC variants, extended by the generated constraints are often significantly easier to solve for state-of-the-art SAT solvers compared to the original formulas. © 2023 MIPRO Croatian Society.

关键词： Binary decision diagrams

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On Active-Set Methods for Quadratic Problems with Positive Semidefinite Matrices 23rd

On Active-Set Methods for Quadratic Problems with Positive...

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23rd International Conference on Mathematical Optimization theory and Operations Research, MOTOR 2024

作者： Vasiliev, Igor Gruzdeva, Tatiana Barkova, Mariia Boyarkin, Denis Iakubovskii, Dmitrii Matrosov Institute for System Dynamics and Control Theory of SB RAS 134 Lermontov str. Irkutsk664033 Russia Melentiev Energy Systems Research Institute of SB RAS 130 Lermontov str. Irkutsk664033 Russia

ISBN: (纸本)9783031733642

Quadratic programming problems (QP) arise in a vast variety of real-world applications in finance, engineering, operational research, and many other fields. A huge number of methods and their various modifications have been developed for solving convex QPs. One of the first algorithms popularized as the solution method for QPs was the active-set method. The main idea of the method is selection of a set of binding constraints (an active set) and then iteratively adaptation it by adding and dropping constraints from the index set. The dual active-set (DAS) method of Goldfarb and Idnani is still well-known to be efficient and numerically stable. Taking advantage of the fact that the unconstrained minimum of the objective function can be used as a starting point of the method, its implementation utilizes the Cholesky and QR factorizations and procedures for updating them. At the same time, it suffers from the restriction that it cannot be applied to problems with positive semidefinite objective matrices, whereas in practice optimization problems may often be of such structure. We propose an add-in to the method of Goldfarb and Idnani that allows solving problems with positive semidefinite matrices directly by the DAS algorithm with a warm-start where a good estimate of the optimal active set is used to start the algorithm. The proposed technique is based on the well-known possibility of representing any matrix, as a difference of two, positive definite ones and solving then a sequence of so-called partially linearized problems. It can be viewed as a particular case of the special local search method for DC minimization problems. A computational experiment to testing the proposed approach was carried out on QPs with positive semidefinite objective matrices from the Maros and Meszaros test set. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

关键词： Iterative methods

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Simulation of Nonlinear Dynamic Processes with Volterra Polynomials and Continued Fractions

Simulation of Nonlinear Dynamic Processes with Volterra Poly...

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2023 International Conference on Industrial Engineering, Applications and Manufacturing, ICIEAM 2023

作者： Solodusha, Svetlana Kokonova, Yuliya Melentiev Energy Systems Institute of Sb Ras Matrosov Institute for System Dynamics and Control Theory Irkutsk Russia Irkutsk National Research Technical University Irkutsk Russia

ISBN: (纸本)9781665475952

In this paper, we propose a technique for increasing the accuracy of modeling nonlinear dynamics of input-output systems using finite segments (polynomials) of Volterra integral power series. We highlight a case when the Volterra kernel identification problem is solved. The linear part of the Volterra polynomials of power N is formed as an equivalent continued fraction. Assuming that the corresponding Volterra kernel is known with some error, such an approach allows us to obtain a model with a new linear part that depends on the error. At the same time, prognostic properties of the integral model can be improved by the using the connection coefficient. The problem of indentifying such a parameter was solved using a special extremal problem. We analyzed the performance of the approach for some dynamic systems. Tests examples were used to compare our approach with the known modeling method that employs a series of Volterra polynomials whose transient responses are tuned to different test signal heights. © 2023 IEEE.

关键词： Transient analysis

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dynamics of Bipartite Logical Networks

Dynamics of Bipartite Logical Networks

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Proceedings of the International Convention MIPRO

作者： G.A. Oparin V.G. Bogdanova A.A. Pashinin Theory of SB RAS Matrosov Institute for System Dynamics and Control Irkutsk Russia

ISBN: (数字)9798350382501

ISBN: (纸本)9798350382518

Based on the Boolean constraints method several problems of qualitative analysis of bipartite logical networks are solved. The dynamics of the trajectories behavior of these networks is studied over a finite time interval. A method is proposed for splitting a bipartite trajectory into two independent trajectories based on deterministic block-sequential updating of the state vectors of each part. Conditions for the existence, isolation and attraction of cyclic trajectories of a given length are obtained as Boolean constraints. The solvability of such equations reduces to the well-known Boolean satisfiability problem, effectual algorithms for solving which provide dynamic analysis for systems with high dimensionality of the state vector over large discrete time intervals. The program modules implementation for building Boolean constraints and checking their feasibility in the form of microservices ensures their reuse, simplification of deployment, updating, and high scalability in the cloud environment. Multi-agent computation management in an applied microservices package provides the non-procedural problem formulation on a distributed model of the subject area, forms and executes a scheme for solving it, and automates the additional resources provision. The practical significance of the obtained results consists in providing the opportunity for a more detailed study of dynamics of the molecular features of gene regulation networks.

关键词： Computational modeling Scalability Heuristic algorithms Biological system modeling Microservice architectures Vectors Mathematical models

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Modeling Agent Behavior in Interacting Microgrids

Modeling Agent Behavior in Interacting Microgrids

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Information Technology and Nanotechnology (ITNT), International Conference on

作者： Igor Bychkov Alexander Feoktistov Mikhail Chekan Matrosov Institute for System Dynamics and Control Theory of SB RAS Irkutsk Russia

ISBN: (数字)9798350372939

ISBN: (纸本)9798350372946

We propose the agent-based approach to intellectualize data processing and analysis in modeling the operations of interconnected microgrids. Microgrids are modern energy systems with a large share of environmentally friendly and resource-saving equipment. The modeling of different aspects for the organization and operation of microgrids is relevant for their structural and parametric optimization. The study of these aspects in the interaction of microgrids deserves special attention. In this case, it becomes possible to take into account the synergistic effect in the distribution and consumption of electric power. We implement the modeling process using a multi-agent system. In this regard, we describe the structure of this system, methods of its construction, and goals and processes of agent operations. In addition, we provide a model of agent behavior developed based on the basis of a finite-state control machine. The advantages of the proposed approach are demonstrated on a model example of balancing generation and consumption of electric power.

关键词： Supply and demand Process control Microgrids Organizations Software Social factors Regulation

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Three Search Algorithms for Three Nonconvex Optimization Problems

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Journal of Mathematical Sciences (United States) 2022年第4期267卷 457-464页

作者： Gornov, A. Yu. Sorokovikov, P.S. Zarodnyuk, T.S. Anikin, A.S. Matrosov Institute for System Dynamics and Control Theory of SB RAS 134 Lermontov Str. Ikrusk 664033 Russian Federation

The paper deals with three numerical approaches that allow one to construct computational technologies for solving nonconvex optimization problems. We propose to use the developed algorithms based on modifications of the tunnel search algorithm, the Luus–Yaakola method, and the expert algorithm. The presented techniques are implemented within the framework of the software package and are used for solving nonconvex optimization problems of various classes, in particular, the minimization of the potential function for the Sutton–Chen atomic-molecular cluster, the problem of parametric identification of nonlinear dynamic systems, and the nonconvex optimal control problem. © 2022, Springer Science+Business Media, LLC, part of Springer Nature.

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